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(ANSYS APDL STRUCTURAL) Modal analysis of a spring-mass system.


Determine the normal and natural frequency of the system below for the values of the masses and the spring stiffness gives. Solution > analysis types mode frequency analysis (ANTYPE = 2) & element type is spring damper element (COMBI 14), Structural mass element (MASS 21).

Assumptions: The spring length is arbitrary selected and are used only to define the spring direction, modal analysis is performed using blocked Lanczos Eigensolver. We get f1=2.5814, f2=8.3263, A1/A2=0.9212, A1/A2=-2.1712 (where A1=NODE 2, A2=NODE 3)

Pre-processor > element type > add/edit/delete > add > structural mass (mass21) > apply > combination > spring damper 14 > ok.

Pre-processor > element type > add/edit/delete> select Mass 21 > options > set (K1 = masses inertias, K2 = parallel to global, K3 = 2-D w/o rot iner) > ok.

Pre-processor > element type > add/edit/delete> select Combi 14 > options > set (K1 = linear solution, K2 = use 2/3D DOF opt, K3 = 2-D longitudinal) > ok > close.

Pre - processor > Pre - processor > real constants> add/edit/delete > add > select (mass21) > ok > enter (real constant set no = 1, 2D mass = 0.5) > ok.

Pre - processor > real constants> add/edit/delete > add > select (mass21) > ok > enter (real constant set no = 2, 2D mass = 1) > ok.

Pre - processor > real constants> add/edit/delete > add > select (combi 14) > ok > enter (real constant set no = 3, K = 200) > ok.

Pre - processor > real constants> add/edit/delete > add > select (combi 14) > ok > enter (real constant set no = 4, K = 200) > ok.

Pre - processor > real constants> add/edit/delete > add > select (combi 14) > ok > enter (real constant set no = 5, K = 800) > ok > close.

Pre - processor > modelling > create > key points > in active cs > enter the below table.

Key point No
X - location
Y - location
Z - location

1
0
0
0
Apply
2
0.5
0
0
Apply
3
1
0
0
Apply
4
1.5
0
0
Ok

Pre - processor > modelling > create > lines > lines > straight lines > select (1-2, 2-3, 3-4) > ok.

Pre - processor > meshing > mesh tool > size control > line set > select line 1-2 > ok > no. of. element divisions = 1 > ok > select line 2-3 > ok > no. of. element divisions = 1 > ok > select line 3-4 > ok > no. of. element divisions = 1 > ok.

Pre - processor > meshing > mesh tool > element attribute > global set > element type number = (combi14), real constant set number (3) > ok > select mesh > select line 1-2 > ok.

Pre - processor > meshing > mesh tool > element attribute > global set > element type number = (combi14), real constant set number (5) > ok > select mesh > select line 2-3 > ok.

Pre - processor > meshing > mesh tool > element attribute > global set > element type number = (combi14), real constant set number (4) > ok > select mesh > select line 3-4 > ok.

Pre - processor > meshing > mesh tool > element attribute > global set > element type number = (mass21), real constant set number (1) > ok > change mesh method to "key point" > select mesh > select key point 2 > ok.

Pre - processor > meshing > mesh tool > element attribute > global set > element type number = (mass21), real constant set number (2) > ok > change mesh method to "key point" > select mesh > select key point 3 > ok.

Solution > analysis type> new analysis > select (modal) > ok.

Solution > analysis type> analysis options > select (block lanczos) in extract method > enter 2 in both, number of modes to extract & in number of modes to expand > ok > start freq = 0, end freq = 0 > ok.

Pre - processor > loads > define loads > apply > structural > displacement > on nodes > select nodes (1&4) > ok > fix UX, UY > apply > again select nodes (2&3) > ok > fix UY > ok.

Solve > current LS > ok > close.

General post processor > result summary  (natural frequency).

General post processor > read results > by pick > select any one (i.e. set 1) > read > close.

Utility menu bar > plot ctrls > animate > mode shape > enter (no of frames = 100, time delay = 0.5, nodal solution data = def+un-deform) > ok.

NOTE: You should get (f1=2.5814HZ & f2=8.3203HZ) which you can see on your left top corner of the GUI.

NOTE: To find the displacement of spring ( General post processor > list results > nodal solution > DOF solution > component of displacement > ok.


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